The advances of social media technologies are significantly changing people's way of connecting with each other, sharing information, and understanding the world. Conventionally, stories and reports from newspapers and magazines provide a primary data source. Nowadays, the emerging social media sharing websites (e.g., Facebook, YouTube, Twitter, Flickr) enable Web users to share easily their personal life and express their opinions at any time. With a rapidly increasing number of users in social media services, the mainstream information source is moving to the Web. There has been a dramatically fast growth of social media data in both volume and topic diversity, which makes social event analysis possible. We consider all the user generated contents as social media data, such as tweets on Twitter, posts on Facebook, images on Flickr, etc. For simplicity of explanation, in this thesis we note all of them as posts.The tremendous boost of online social media data enables identification of popular events before the mainstream media, which can be potentially used in real-time notification of emerging events.Notifying mobile users of fires and crimes happening nearby is one example. It may also offer opportunities to governments for timely responses to urgent events at various stages. Furthermore, events are often not isolated. New events may keep coming up successively as a consequence of an initial event, whereas the topic focus on the subsequent events may shift due to the event evolvement.Modelling the implicit relationships among events could help better understand the event evolution process and predict future events. After an event is identified, it is unnecessary to present all related posts about the event to the public. Website users usually prefer to view the event with several representative posts rather than all of them. A cover with selected posts would help users better understand and recall the event. This leads to the problem of how to efficiently and effectively find representatives for events.The first task in this thesis is identifying social events. Social event identification utilizes social media data to detect events and plays a critical role in many applications. For example, early warnings of impending natural disasters or disease are necessary for the safety and security of populations within the affected areas. Therefore, under a variety of situations, there is a demand to derive an effective approach to identify events and report to the public. In this task, we propose a novel approach for identifying events from social media data according to their spatio-temporal context and textual information. To better capture the extensibility of social events in both spatial and temporal space, spatio-temporal expansions are employed.The second task is modelling relationships among events. We observe that different events may tell different stories under the same topic and narrate the development of a topic together. In other words, a growing topic is composed of a series of relevant events,...